String Field Theory and Background Independence?

I've recently been reading about string field theory (note: I'm a novice). As I understand, the string field is an infinite collection of classical fields. But I'm uncertain as to why this formulation leads to background independence?

The word "background independance" doesn't really mean what you might think it does. In general, be careful about how people define it and in what context you are in, b/c there is a lot of fog (particularly on the internet) about what people really mean. In general proffessionals rarely use the terminology unless they're pitching an advertisement, mostly b/c its ambiguous.

Now, SFT is background independant in the same sense that Maxwells equations are. Everything is dynamical, there is no fixed structure that cannot be varied, everything can be written in terms of forms, potentials and field strengths.

In another sense, SFT is no more or no less background independant or dependant than regular string theory, b/c it essentially just reproduces perturbation series and *might* miss some (but not all) of the nonperturbative 'backgrounds' that also must exist in a full theory.

Be aware there are several versions of string field theory, like covariant SFT or another that is confusingly called 'background independant open SFT'. Its best to think about what exactly the objects are that they are quantizing (second quantization, third quantization etc) eg string fields, spaces of 2dim conformal field theories, etc. Its also an advanced subject that I don't recommend to novices until you have a lot of ... wait for it.. background material.

In another sense, SFT is no more or no less background independant or dependant than regular string theory, b/c it essentially just reproduces perturbation series and *might* miss some (but not all) of the nonperturbative 'backgrounds' that also must exist in a full theory.

To write the string action, you have to pick up some background spacetime metric (usually taken to be flat). To write the string-field action (e.g., Witten's cubic bosonic open-string-field action), you don't have to pick up some background spacetime metric. Doesn't it mean that string field theory is more background independent than regular string theory?

Yea, see point 1, but they're also shown to be equivalent theories. Again it depends how you define BI. You could say SFT is manifestly BI, and regular ST manifestly BD, but in terms of what it tells you about the full nonperturbative theory (where the metric tensor is emergent), it does no better or worse (in fact, sometimes it does better and sometimes it does worse). Even that last statement I wrote is confused, b/c of dualities and other technical details.

The point is its really just semantics at the end of the day and what you want to compute.

Perhaps they are equivalent perturbatively, but not non-perturbatively. For example, tachyon condensation (which is a non-perturbative effect) can be obtained from Witten's cubic string field theory, but not from "regular" string theory.

The way I understand it, picking a background is the same as picking a guage, if you were working in a run of the mill Yang-Mills theory. So it seems odd that physical things that you can compute should turn out differently in one case vs. the other.

I see the logic in Ben's statement, and I think it focuses on the general issue (regardless if we're talking about string theory or some other theory). This "issue" and sometimes paradox of BI vs BD is I think a general problem and not a problem just for string theory. There IMO are problems also in other theories. In a certain sense, to do away with ALL backgrounds is a certain sense also prolbemativ, because what are you refering to? I think the problem is more difficult thta these extrems.

From the point of view of the "fundamental symmetry" and the equivalence class of all distinctions generate by a set of transformations, the choice of element(gauge choice) is completely arbitrary and should not change the "physics" determined by the symmetry itself.

I think a problem is that it seems (to me) common to view the existence of equivalence classes in a realist sense.

Ie. the question is thus, IS the actual physics determined by a fundamental symmetry? and how is that conceptually consistent with the modern non-realist idea of quantum interactions which usually suggest that physical interactions correspond to relative information?

Could it instead me that one can, due to constraints of nature, not pick a gauge AND maintain an undistorted view of the fundamental symmetry at the same time? Ie. perhaps there is a kind of uncertaintly principle here, where from the gauge fixed point of view, the symmetry is not fundamental after all, it's only emergent.

Ben, even if I got your intention wrong (I don't mean to suggest you said something you didn't!), I would still raise the issue I tried to described as important, even outside of string theory. Give or take some details I made an association to your comment.

The issue exists also in classical GR and it's diff.symmetry. But there the issues is usually a non-issue since it's a realist type of theory. But in a measurement theory of it, the question is what parts that really are the physical observables. In the classical theory this isn't an issue. Because there is realism. But then the problem becomes a conceptual one.

I guess my original question was whether string field theory can be considered to be background independent in a general relativistic sense? If string field theory is string theory reformulated in the language of quantum field theory, and QFT is background dependent, how does the background independence in SFT arise?

If we consider the string field as an infinite sum of classical fields, can the classical fields be considered background independent? I'm somewhat confused by Haelfix's comment that Maxwell's equations are background independent - Haelfix, could you expand on this?

Sorry for all the questions! The forums have been very helpful so far.

Maxwells equations without sources reads like 0 = dF = d*F. Where F is the two form F = dA, A is the gauge connection and * is the hodge star operator.

These field equations are manifestly background independant, no background is specified or involved in the dynamics and the domain of validity is arbitrary up to that which is induced by the hodge star (technically it adds structure to the dual space).

This particular formalism can live in curved space, flat space etc etc You are free as well to write Maxwells equations in a manifestly background dependant way as well in terms of the more familiar fields B(X,t) and E(X,t) where this choice spontanously breaks the diffeomorphism symmetry of the manifold where we want the field equations to live in.

In a sense, BI is completely trivial here. Varying the manifolds base space metric does not change the validity, form and universality of the solution.

And that the equations can be written in a rotationall invariant manner does not imply rotations are a symmetry - solutions of these equations related by a rotation are NOT physically equivalent - that is, rotations are not symmetry.

Any equations can be be put into a generally covariant form but that does not mean that general covariance are a symmetry. The point about GR, as apposed to other theories, is that its solutions, related by diffomorphisms, are physically equivalent.

I dont think there is a lot of fog around the defintion of BI. I think there is just fog around people's understanding of it. I wrote a section on BI for wiki on the subject of in the hope to clar up the understanding.

“Finding the right framework for an intrinsic, background independent formulation
of string theory is one of the main problems in string theory, and so far has remained out
of reach.” ... “This problem is fundamental because it is here that one really has to address the question of what kind of geometrical object the string represents.”

I'm sure he wouldn't have made this statement if ST was only non-manifestly BI but BI all the same

When String theorists talk about background independance, they're referring to their configuration space. Eg every part or corner is ideally described using the same language. The point being, that language does not exist yet, and thats what Witten is talking about.

Now, in one corner of the configuration space of string theory, AdS/CFT lives and is valid. In that regime, it is often said to be completely BI (where here we have chosen a new definition for the word background, different than the former and closer in spirit to the GR meaning), but in the more general context it is still BD.

You have to understand, in no sense is what string theorists talking about, the same as the backgrounds the LQG people are talking about. Its really just a statement of formalism moreso than a physical statement.

Furthering the confusion are differing definitions (not just of what is or is not a background). So for instance, people will often say QFT is background dependant. But thats misleading too, it is trivial for me to write down a topological field theory, or a 2+1 dim QFT that is exactly soluble, either using perturbation series (resumming) or without. So then we have to expand what we are talking about to 'manifest' vs 'nonmanifest' and somehow it seems to simply be a statement about 'perturbative' vs 'nonperturbative' or 'before calculation' and 'after calculation'.

Yet another, completely different definition that i've seen used in the past is more akin to the difference between (active/passive) diffeomorphisms.

Bottomline, the whole thing is horribly vague, and context dependant and sensitively depends on the definition. Where it becomes really illdefined is the second people start comparing completely different classes of theories.

Bottomline, the whole thing is horribly vague, and context dependant and sensitively depends on the definition.

I'm just an amateur, but I agree with this.

The following is my own opinion and it does not necessarily relate to anthing Haelfix meant to say, but I personally think this relates to some deeper reflections of background independence and the quest for new logic, that smolin (appears to me) to have sniffed. In a certain sense one could also refer to the CONTEXT as a "background", and part of the implicit references, such as the choice of logic and langauges.

In this for admittedly more obscure and abstract version of "background", not even GR in background independent IMHO, because there are still background references, such as the manifold etc. This is one conceptual objection I have to classical GR and classical physics in general. These background "structures", manifolds or whatever, does not fit in the grand vision of information processing, which does not allow for "hidden background information", and ultimately this seems to trace down to logic itself.

It's easy to get a feeling that your head is spinning and this nothing but circular reasoning - there seems to be no static acceptable reference. Now, the question is if that is such a bad thing? If we look around us? I think it's a hint. Maybe we just need to find out how to tame the circular madness, and turn it into evolutionary progression?

This is what I hope, and it's the spirit that I personally see in some of Smolins crazy papers. And there the observation that the notion of BI seems fundamentally context-relative, may be one of the key observations to progress? If even physical law is evolving, we seem to have lost all connection to solid ground.

Not trying to be funny but in short I think a good way of expressing what I tried to expand upon is that in this generalise sense, paradoxally, the notion of background-independence is itself background dependent. This is a nutshell describes IMHO at least, the problem.

I *think* this is pretty much what Healfix said in his last paragraph, if you extend the concept of background to include ALL backgrounds (including "definitions", which are rarely as innocent as they sound, since the involve choices).

Not trying to be funny but in short I think a good way of expressing what I tried to expand upon is that in this generalise sense, paradoxally, the notion of background-independence is itself background dependent...

What I find of primary interest is what researchers are trying to achieve, it is only of secondary importance what words they use to refer to their goal.

For many years, nonstring quantum gravity researchers used the words "background independence" as a kind of flag to help distinguish their work from string and to identify one of the main aims of their research. But lately the phrase has become involved in a verbal tug-of-war, with string thinkers adopting it and giving it a special meaning within stringy context. So instead of promoting communication, the phrase can now lead to sterile discussions---about who gets to control this bit of verbal turf and impose their own meaning on it, wear it as a badge of honor, etc.---and about what is the "real meaning" of the words, as if they stood for some permanent abstract concept.

For the quantum gravity researchers, one solution to the verbal tug-of-war has simply been to stop relying on the words "background independence", and find other ways of stating their overall goal.

So for example when Carlo Rovelli was invited to come to the annual Strings-2008 conference in August and give an overview talk on Loop Quantum Gravity (and related approaches) he did not once use the phrase "background independence". Here is the video:http://cdsweb.cern.ch/record/1121957?ln=en

When, at the beginning of his talk, he needed to state the main motivation of the LQG program and address the question Why Loops? he used different words. He said something like this: The central problem LQG addresses is how to describe the fundamental degrees of freedom of a QFT when there is no fixed background spacetime.

Abhay Ashtekar has made a similar departure. See for example his October 2008 31-page overview of Quantum Space-times to be published in a book commemorating the Minkowski centennial. http://arxiv.org/abs/0810.0514
He describes the main aim of his community's research program at the start without using the debased terminology.

Once near the end, at the top of page 27 (last page of text) he uses the phrase, but there it is merely shorthand for what has already been described and discussed at length. In his statement of purpose at the beginning he avoids the corrupted abstraction and spells things out this way

==quote Ashtekar, page 3==
Over the last 2-3 years several classically singular space-times have been investigated in
detail through the lens of loop quantum gravity (LQG) [2–4]. This is a non-perturbative
approach to the unification of general relativity and quantum physics in which one takes
Einstein’s encoding of gravity into geometry seriously and elevates it to the quantum level.
One is thus led to build quantum gravity using quantum Riemannian geometry [5–8]. Both
geometry and matter are dynamical and described quantum mechanically from the start.In particular, then, there is no background space-time. The kinematical structure of the
theory has been firmly established for some years now. There are also several interesting
and concrete proposals for dynamics (see, in particular [2–4, 9]). However, in my view there
is still considerable ambiguity and none of the proposals is fully satisfactory. Nonetheless,
over the last 2-3 years, considerable progress could be made by restricting oneself to subcases
where detailed and explicit analysis is possible [10–15]. These ‘mini’ and ‘midi’ superspaces
are well adapted to analyze the deep conceptual tensions discussed above. For, they consider
the most interesting of classically singular space-times —Friedman-Robertson-Walker
(FRW) universes with the big bang singularity and black holes with the Schwarzschild-type
singularity— and analyze them in detail using symmetry reduced versions of loop quantum
gravity. In all cases studied so far, classical singularities are naturally resolved and the
quantum space-time is vastly larger than what general relativity had us believe. As a result,
there is a new paradigm to analyze the old questions.
The purpose of this article is to summarize these developments,...
==endquote==

As you can probably guess, Lee Smolin is not relying heavily on the phrase either. For instance he gave a seminar talk at the ILQGS on 21 October which did not use the phrase at all.http://relativity.phys.lsu.edu/ilqgs/
Instead, in the first part of the talk he chose to discuss three different levels or meanings of the emergence of spacetime. I will quote just his first two:
==quote Smolin 21 October slide #3==
What do we mean by emergence of space‐time?

Emergence of the manifold: The fundamental description
of nature does not involve fields (quantum or classical)
on a differential manifold.

Emergence of the classical metric: The fundamental
description of nature does not involve a classical metric field.
...
...
==endquote==
Here the main issue seems to me a clear and practical one: does your description use differential manifolds or not? And if it does use a manifold, do you or don't you specify a classical metric on it, giving it a fixed geometry?

=======================
EDIT: As an afterthought, prompted in part by Fra's next post, I should say that I gave these links primarily as examples to illustrate the point that representative QG people (Rovelli, Ashtekar, Smolin) were not using the phrase "background independence", or were depending on it less these days.
Rovelli's talk at Strings-2008:http://cdsweb.cern.ch/record/1121957?ln=en
Ashtekar's October 2008 survey overview essay "Quantum Space-times":http://arxiv.org/abs/0810.0514
Smolin's October 2008 seminar talk:http://relativity.phys.lsu.edu/ilqgs/
I just wanted to provide these links as evidence, in case any reader had trouble believing the point I was making.

I didn't want to make extra work, if you didn't need convincing, or perhaps already knew about that shift in vocabulary. In fact the talks and the essay are interesting in their own right, I think, but the links were just brought in as evidence to corroborate.

Three or four years ago, the vocabulary was different. B.I. meant "does not use a fixed metric" or "does not use a differential manifold". And Ashtekar would write a survey called "The Status of Background Independent Quantum Gravity". That was the flag the community waved to identify itself and distinguish itself from string.

But then string theorists basically grabbed the other guys' flag, and gave it a different meaning, and made a big noise about it, so there was enough confusion that it was no longer useful as a concise identifier any more. So QG people now use the term less---or depend on it less. They still use the words on occasion, but they use other words as well, so that they no longer rely on B.I. to have a clear meaning without further explanation. That's my take on it anyway.